Convergence analysis of the improved θ-scheme for two-dimensional double singular stochastic Volterra integral equations

Abstract

This study contributes to the understanding of the behavior of two-dimensional double singular
stochastic Volterra integral equations (DSSVIEs) and provides a comprehensive analysis of their properties.
The evaluation of well-posedness, convergence, and the introduction of a numerical technique such as
the improved θ-scheme (ITS) for solving the equation offer valuable insights for future research in this
field. The proposed improvement utilizing sum-of-exponentials (SOE) approximation promises enhanced
computational efficiency, which is crucial for practical applications. Overall, this study advances the
knowledge of two-dimensional DSSVIEs and provides a solid foundation for further investigation and
development in this area. An example is presented to demonstrate the effectiveness of the results achieved.